Terminology

The practice of writing “∞\infty-sheaf” instead of ∞-stack is a rather reasonable one, since a stack is nothing but a 2-sheaf.

Notice however that there is ambiguity in what precisely one may mean by an ∞\infty-stack: it can be an (∞,1)(\infty,1)-sheaf or more specifically a hypercomplete(∞,1)(\infty,1)-sheaf. This is a distinction that only appears in (∞,1)-topos theory, not in (n,1)-topos theory for finite nn.